Solve the equation.

Question

log1/5(x^2+x)-log1/5(x^2-x)=-1

x=

Answer 1

log1/5(x^2+x)-log1/5(x^2-x) = -1

log a - log b = log(a/b)

10(x²+x) = x²-x

10x²+10x = x²-x

9x²+11x = 0

x(9x+11) = 0

x = 0 or 9x+11 =0

x = 0 , x = -11/9 

 

Check

For x=0 the function is undefine 

For x=-11/9 ⇒ -1.26 + 0.26 = -1

So the solution is x = -11/9